Question 205562
First of all by using the A=lw equation you are throwing in a new variable A which you aren't given so that's not the best course to take
It seems to me that the easiest way to solve this problem would be to use triginomitry, if you haven't taken that class i'm sorry i'll do my best to explain it thoroughly.
- OK first let's label the sides as x and y (we only need two variables because there are only two different side lengths
- because one side is 2 meters longer than the other we can state the following
{{{y = x+2}}}
- So now our two sides are x and x+2
- since they state that the diagonal is 10m we know that drawing the diagonal in the rectangle makes 2 right triangles
- we only need one of the triangles so now we have one triangle that has a hypotenuse of 10 and the other two sides are x and x+2
- since we don't know any of the angles we can't use sin, cos, tan or the like
- we can however use the pythagorean therum which states that
-  {{{a^2 + b^2 = c^2}}}
-  where a and b are the sides and c is the hypotenuse
- now we can plug in our values for all three sides
-  {{{(x)^2+(x+2)^2 = (10)^2}}}
- then just simplify the equation
-  {{{x^2 + (x+2)(x+2) = 100}}}
-  {{{x^2 + x^2 + 4x + 4 = 100}}}
-  {{{2x^2 + 4x + 4 - 100 = 100 - 100}}}
-  {{{2x^2 + 4x - 96 = 0}}}
-  Now we can factor to solve for x
-  {{{(2x -12)(x+8) = 0}}}
-  {{{2x-12 = 0}}} and {{{x+8 = 0}}}
-  {{{2x = 12}}}   and {{{x = -8}}}
-  {{{x = 6}}}     and {{{x = -8}}}
- Since we can't have a negative side length the only answer is 6
- So now that {{{x = 6}}}, {{{y = (6) + 2}}}
-                          {{{y = 8}}}
- So now we know the lengths of the other sides
- {{{x=6}}}and{{{y=8}}}